Question

solve the equatoin bye factorisation method 2x^2+5√3x+6=0​

Answer 1

Solution :-

$\longrightarrow 2 {x}^{2} + 5 \sqrt{3} x + 6 = 0 \\ \\ \longrightarrow 2 {x}^{2} + 4 \sqrt{3} x + \sqrt{3} x + 6 = 0 \\ \\ \longrightarrow 2x(x + 2 \sqrt{3} ) + \sqrt{3} (x + 2 \sqrt{3} ) = 0 \\ \\ \longrightarrow (2x + \sqrt{3} )(x + 2 \sqrt{3} ) = 0$

Now, the Roots are →

$\bullet 2x + \sqrt{3} = 0 \\ \\ \longrightarrow 2x = - \sqrt{3} \\ \\ \longrightarrow x = - \frac{ \sqrt{3} }{2}$

$\bullet x + 2 \sqrt{3} = 0 \\ \\\longrightarrow x = - 2 \sqrt{3}$

So, the Roots of given polynomial are (-√3/2) and (-2√3).